Pith Number

pith:GGRZVRYT

pith:2012:GGRZVRYT54JFDZVTQGRTNDHGKF

not attested not anchored not stored refs pending

The cocycle condition for multi-pullbacks of algebras

Bartosz Zielinski, Piotr M. Hajac

arxiv:1207.0087 v1 · 2012-06-30 · math.QA · math.RA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GGRZVRYT54JFDZVTQGRTNDHGKF}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:52:00.387901Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31a39ac713ef1251e6b381a3368ce65152952a2e4bac835b02cfe99d29678468

Aliases

arxiv: 1207.0087 · arxiv_version: 1207.0087v1 · doi: 10.48550/arxiv.1207.0087 · pith_short_12: GGRZVRYT54JF · pith_short_16: GGRZVRYT54JFDZVT · pith_short_8: GGRZVRYT

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GGRZVRYT54JFDZVTQGRTNDHGKF \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 31a39ac713ef1251e6b381a3368ce65152952a2e4bac835b02cfe99d29678468

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "976d3b836d715261d7b3bbe3afbf14afbc7c12baca7057afc35b147775caad99",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2012-06-30T12:50:16Z",
    "title_canon_sha256": "a59f6b79551ebc3dd71ef5bea6ce76f7f89059f494cc1c233cc0a76b55c05f22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0087",
    "kind": "arxiv",
    "version": 1
  }
}